There are certain phenomena on our earth which have great significance from military and/or commercial points of view. One such phenomenon is the water temperature of the oceans or other large bodies of water. Knowing the temperature of the water over large areas is of importance for military purposes, as well as from a commercial point of view, since ocean water temperature affects commercial fishing. Theoretically, one can take direct measurements of the water temperature at specific locations. However, due to the large surface area of the oceans, taking direct water temperature measurements over any large surface area of hundreds of thousands of square miles is clearly impractical.
Similarly, cloud measurements in general, and more particularly, ice particle size measurements of cirrus clouds, are also important in imaging certain bodies in order to remove or limit interfering clouds from any satellite images, as well as to obtain measurements of precipitation occurring within the atmosphere. Satellite sensor instruments have been used to measure specified radiance of certain ground-based bodies to within a specified error. That is, the satellite sensors themselves make known radiance measurements at the top of the atmosphere of bodies located at the earth's surface, such as water temperature.
However, the goal is to determine a given Environmental Data Record (EDR) or surface parameter to within a specified error. It is therefore crucial to relate the radiance measurement errors, which we know how to predict, to the expected errors in the EDR's. For many EDR's it is relatively easy to create forward models which, given specific values of the EDR parameters, predict the radiance leaving the top of the atmosphere. What is not so easy, however, is to exercise these models over a range of environmental parameters large enough to find the level of radiance error which produces adequate EDR estimates. Fortunately, as will be shown herein, signal processing formulas applied to linearized versions of an EDR forward model, permit one to proceed directly from the known radiance error (i.e. the satellite sensor noise of the point design) to the expected errors in the EDR. These formulas also specify algorithms, based on the linearized forward model, which can be used to estimate EDR's from their associated radiances.
As will be shown in the detailed description below, a basic statistical methodology for connecting EDR errors to radiance measurement errors will be presented in Section 1, followed by two examples in Sections 2 and 3 showing how to deal with VIIRS-based EDR's when the forward models can be written down algebraically. The Sea-Surface Temperature EDR analyzed in Section 2 shows that the predicted EDR error using the method disclosed herein matches NOAA's past experience. This provides support that the statistical methodology works as expected. The cirrus cloud EDR analyzed in Section 3 shows how the methodology can be used to analyze the performance different versions of an EDR algorithm. Section 4 shows how to handle EDR's where only a computerized version of the forward model (such as MODTRAN or FASCODE) exists. The technique described in Section 4 applies equally well, of course, to those VIIRS-based EDR's where only computerized versions of the forward model are easily available.